SciPost Phys. Proc. 6, 017 (2022) ·
published 31 May 2022
It has been suggested that the Landau-gauge gluon propagator has complex
singularities, which invalidates the K\"all\'en-Lehmann spectral
representation. Since such singularities are beyond the standard formalism of
quantum field theory, the reconstruction of Minkowski propagators from
Euclidean propagators has to be carefully examined for their interpretation. In
this talk, we present rigorous results on this reconstruction in the presence
of complex singularities. As a result, the analytically continued Wightman
function is holomorphic in the usual tube, and the Lorentz symmetry and
locality are kept valid. On the other hand, the Wightman function on the
Minkowski spacetime is a non-tempered distribution and violates the positivity
condition. Finally, we discuss an interpretation and implications of complex
singularities in quantum theories, arguing that complex singularities
correspond to zero-norm confined states.
SciPost Phys. Proc. 6, 013 (2022) ·
published 31 May 2022
In this talk we want to discuss the color confinement criterion which guarantees confinement of all colored particles including dynamical quarks and gluons.
The most well-known criterion is the Kugo-Ojima color confinement criterion derived in the Lorenz gauge.
However, it was pointed out that the Kugo-Ojima criterion breaks down for the Maximal Abelian gauge in which quark confinement has been verified according to the dual superconductivity caused by magnetic monopole condensations.
We give the color confinement criterion based on the restoration of the residual local gauge symmetry which can be applied to the Abelian and non-Abelian gauge theories as well irrespective of the compact or non-compact formulation,
and enables us to understand confinement in all the cases.
Indeed, the restoration of the residual local gauge symmetry which was shown by Hata in the Lorenz gauge to be equivalent to the Kugo-Ojima criterion indeed occurs in the Maximal Abelian gauge for the SU(N) Yang-Mills theory in two-, three- and four-dimensional Euclidean spacetime once the singular topological configurations of gauge fields are taken into account.
This result indicates that the color confinement phase is a disordered phase caused by non-trivial topological configurations irrespective of the gauge choice.